Existence of ground states for negative ions at the binding threshold

TL;DR

This paper proves the existence of ground states for negative ions at the critical nuclear charge, showing electrons remain bound and the system's radius stays finite at the binding threshold.

Contribution

It establishes the conditions under which a ground state exists at the critical charge, advancing understanding of atomic stability at the binding threshold.

Findings

Ground state exists at Z_c under certain conditions

Electrons remain bound at the critical charge

System radius remains finite at Z_c

Abstract

As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition at some critical Z_c. We investigate whether the electrons remain bound when Z=Z_c and whether the radius of the system stays finite as Z_c is approached. Existence of a ground state at Z_c is shown under the condition Z_c<N-K, where K is the maximal number of electrons that can be removed at Z_c without changing the ground state energy.